To determine the Consumer Price Index (CPI) for Year 2, we need to follow a series of steps. The CPI measures the average change in prices over time that consumers pay for a basket of goods and services.
1. Identify the Basket of Goods:
- The basket consists of 1 bottle of shampoo and 2 bars of soap.
2. Determine the Prices for Year 1:
- Price of 1 bottle of shampoo: [tex]$6.50
- Price of 1 bar of soap: $[/tex]1.25
3. Calculate the Total Cost of the Basket in Year 1:
- [tex]\( \text{Cost}_{\text{Year 1}} = (\text{Price of 1 bottle of shampoo} \times \text{Quantity of shampoo}) + (\text{Price of 1 bar of soap} \times \text{Quantity of soap}) \)[/tex]
- [tex]\( \text{Cost}_{\text{Year 1}} = (6.50 \times 1) + (1.25 \times 2) \)[/tex]
- [tex]\( \text{Cost}_{\text{Year 1}} = 6.50 + 2.50 = 9.00 \)[/tex]
4. Determine the Prices for Year 2:
- Price of 1 bottle of shampoo: [tex]$6.60
- Price of 1 bar of soap: $[/tex]1.30
5. Calculate the Total Cost of the Basket in Year 2:
- [tex]\( \text{Cost}_{\text{Year 2}} = (\text{Price of 1 bottle of shampoo} \times \text{Quantity of shampoo}) + (\text{Price of 1 bar of soap} \times \text{Quantity of soap}) \)[/tex]
- [tex]\( \text{Cost}_{\text{Year 2}} = (6.60 \times 1) + (1.30 \times 2) \)[/tex]
- [tex]\( \text{Cost}_{\text{Year 2}} = 6.60 + 2.60 = 9.20 \)[/tex]
6. Calculate the CPI for Year 2:
- The CPI for Year 1 is considered the base year and is set to 100.
- [tex]\( \text{CPI}_{\text{Year 2}} = \left( \frac{\text{Cost}_{\text{Year 2}}}{\text{Cost}_{\text{Year 1}}} \right) \times 100 \)[/tex]
- [tex]\( \text{CPI}_{\text{Year 2}} = \left( \frac{9.20}{9.00} \right) \times 100 \)[/tex]
- [tex]\( \text{CPI}_{\text{Year 2}} = 1.0222 \times 100 \)[/tex]
- [tex]\( \text{CPI}_{\text{Year 2}} = 102.22 \)[/tex]
Therefore, the CPI for Year 2 is 102.22.
